# Normal distribution and confidence intervals

• Sep 25th 2012, 12:10 PM
StephenB1965
Normal distribution and confidence intervals
Hello,

I am looking for a little guidance or help with the following question:

The standard deviation of the masses of 600 blocks is 248 kg.
A random sample of 55 blocks has a mean mass of 4.72 Mg.
With what degree of confidence can it be said that the mean mass of all the blocks is 4.72 ± 0.100 Mg?

I've tried reading up some information on the normal distribution table but can't really get my head around it. Could anyone offer me some advice or provide me with a good link with information on the subject?

Thanks.
• Sep 25th 2012, 05:44 PM
SlipEternal
Re: Normal distribution and confidence intervals
I am not an expert on this stuff, but I think you need to figure out the standard error for your sample. Once you know standard error, you can use it to judge how close your estimate for the mean should be and with what confidence level. Essentially, standard error is the standard deviation of your sample. So, if you were to find the mean mass of every possible sample (from 1 block, all the way up to 600 blocks), you should be able to calculate the approximate standard deviation of the set of samples based on the actual standard deviation of the masses and the size of your sample. So, using the binomial theorem, since your sample is greater than 30 blocks, you can use the formula that standard error is standard deviation over the square root of your sample size.

$\text{St Err}=\frac{\sigma}{\sqrt{n}}$

Where $\sigma$ is your standard deviation of 0.248Mg=248kg, and your sample size $n=55$. Need any more assistance?
• Sep 25th 2012, 07:44 PM
MaxJasper
Re: Normal distribution and confidence intervals
Quote:

Originally Posted by StephenB1965
The standard deviation of the masses of 600 blocks is 248 kg.
A random sample of 55 blocks has a mean mass of 4.72 Mg.
With what degree of confidence can it be said that the mean mass of all the blocks is 4.72 ± 0.100 Mg?...

Assuming a normally distributed population without replacement samples:

Population size = N =600
Sample size =n = 55
$\sigma =248$

then, sample standard error:

$s=\frac{\sigma }{\sqrt{n}}*\sqrt{\frac{\text{N}-n}{\text{N}-1}} = 31.897$

and z value is:

$z=\pm \frac{100}{s}=\pm 3.1351$

Now find probability from a normal distribution table.
• Sep 27th 2012, 06:49 AM
StephenB1965
Re: Normal distribution and confidence intervals
Many thanks but I thought the sample standard error was calculated by:
http://onlinestatbook.com/chapter8/graphics/sem_pop.gif
• Sep 27th 2012, 01:34 PM
JungleMath
Re: Normal distribution and confidence intervals
StephenB1965,

I am also looking for how to figure out confidence intervals when I only have a mean of a sample and a SD of the population. If you get any luck, drop me a message :) will keep checking this post though.

Also, I thought the standard error of the mean was

SE = Standard Error of Population Mean
SD = Standard Deviation of Population

SE = SD/sqrrt(SampleSize)
• Sep 27th 2012, 01:54 PM
JungleMath
Re: Normal distribution and confidence intervals
Quote:

Originally Posted by MaxJasper
and z value is:

$z=\pm \frac{100}{s}=\pm 3.1351$

Now find probability from a normal distribution table.

MaxJasper, what is the z value for?
• Sep 27th 2012, 02:13 PM
MaxJasper
Re: Normal distribution and confidence intervals
Quote:

Originally Posted by JungleMath
MaxJasper, what is the z value for?

http://www.pearsonclinical.co.uk/Sit...stribution.jpg
• Sep 27th 2012, 02:25 PM
JungleMath
Re: Normal distribution and confidence intervals
Thank you very much, helped out alot.
• Sep 28th 2012, 05:16 AM
StephenB1965
Re: Normal distribution and confidence intervals
Thanks for your help so far MaxJasper, one quick query tho, to get the s value (which I presume is the sample standard error) why do you have to multiply the standand error by √N – n / N - 1?
• Sep 28th 2012, 08:18 AM
MaxJasper
Re: Normal distribution and confidence intervals
Normal distribution assumes N=infinite, when N<inf then the modified version is used for sample standard error.